Semions

Semions are a type of anyon, quasiparticles that can emerge in two-dimensional quantum systems and that obey fractional statistics. When two identical semions are exchanged, the many-body wavefunction acquires a phase factor of i, which is neither +1 as for bosons nor -1 as for fermions. This corresponds to an exchange angle of pi over two and a topological spin of 1/4.

Semions are Abelian anyons. In the simplest model, the theory contains two sectors: the identity and a semion, with the fusion rule that two semions fuse to the vacuum (s × s = 1). Consequently, exchanging two semions yields the phase i, and the semion is typically treated as its own antiparticle in this minimal framework.

Physical realizations of semionic statistics occur in certain two-dimensional topological phases. The bosonic Laughlin state at filling factor one-half is a canonical example where semionic excitations can arise. The low-energy effective field theory describing such a phase is often formulated as a U(1) Chern-Simons theory at level two, which reproduces the braiding and fusion properties of the semion.

Experimental detection of semions typically involves interferometric measurements designed to reveal braiding-induced phase shifts. While fractional quantum Hall experiments provide strong evidence for anyons in general, unambiguous identification of pure semionic statistics remains an area of active investigation.

See also: anyons, fractional statistics, topological order, Chern-Simons theory.